Definition:Inverse Cosine/Terminology
Terminology for Inverse Cosine
There exists the popular but misleading notation $\cos^{-1} x$, which is supposed to denote the inverse cosine function.
However, note that as $\cos x$ is not an injection (even though by restriction of the codomain it can be considered surjective), it does not have a well-defined inverse.
The $\arccos$ function as defined here has a well-specified image which (to a certain extent) is arbitrarily chosen for convenience.
Therefore it is preferred to the notation $\cos^{-1} x$, which (as pointed out) can be confusing and misleading.
Sometimes, $\operatorname{Cos}^{-1}$ (with a capital $\text C$) is taken to mean the same as $\arccos$.
However, this can also be confusing due to the visual similarity between that and the lower case $\text c$.
Some sources hyphenate: arc-cosine.